The government actually isn't asking it to do so, but to write new software to defeat a feature that locks the phone if too many incorrect passwords are entered.

If forced to do so, there's danger that the software could escape into the wild, threatening security of information on every iPhone in the world, Cook argues.

Other tech giants are supporting Apple.

"We stand with @tim_cook and Apple (and thank him for his leadership)!" tweeted Jack Dorsey, Twitter CEO Thursday afternoon. Facebook said it condemns terrorism and supports law enforcement, but will "fight aggressively" against requirements for companies to weaken the security of their systems.

Not everyone supports Apple's stand, saying it places higher value on privacy than national security.

A former National Security Agency and another Brookings Institution fellow said Apple's "self-presentation as crusading on behalf of the privacy of its customers is largely self-congratulatory nonsense."

But we're not sure anyone associated with the NSA is an authority on the civil liberties Cook supporters are trying to protect.